Abstract: Let be an inverse sequence of spaces and maps satisfying (i) each has the homotopy type of a CW complex, (ii) each is a Hurewicz fibration, and (iii) the connectivity of the fiber of goes to with . Let be the inverse limit of the sequence. It is shown that the natural homomorphism (from Čech cohomology to singular cohomology, with ordinary coefficient module ) is an isomorphism for all . It follows that for any Eilenberg- Mac Lane space . It is also shown that, except in trivial cases, does not have the homotopy type of a CW complex.